Relevance of Filter Bank Multi-Carrier (FBMC) systems along with Offset Quadrature Amplitude Modulation (OQAM) for 5G Radio Access Technology (RAT) cannot be ruled out. FBMC-OQAM modulation technique has many attractive features over OFDM that make it more appealing to be the radio waveform in 5G. However, being a multi-carrier modulation technique, it has high PAPR and prone to spectral regrowth in the presence of a non-linear high power amplifier (HPA), which is a vital component in contemporary modern communication systems. This spectral regrowth indicate that the excellent frequency localization property of the FBMC-OQAM signals no longer holds in the presence of a non-linear HPA. So, there is a dire need to predict the extant of spectral regrowth induced by the HPA non-linearities. With cumulants, it is possible to predict the power spectral density (PSD) of the HPA output. Prediction of spectral regrowth in the case of OFDM systems was already done and in this paper it is extended to FBMC based systems. HPA of Salehs model is used for simulations but prediction can be done for any measured or modeled HPA after polynomial fitting of its AM/AM and AM/PM distortion characteristics.